In the other category, phase shifts, optimized based on S-CSI, do not need to change at every coherence interval but every several intervals. Compared to I-CSI, this method offers lower feedback overhead due to less frequent phase optimization, especially when the numbers of BS antennas and IRS elements are large. Moreover, the feedback overhead reduction results in less power consumption by the IRS controller and release of the capacity requirement for the IRS control link. Furthermore, a significant computational complexity reduction is achieved at the BS, which needs to update the phase shift matrix at a much larger time scale compared to phase shift matrix update in I-CSI schemes that occurs at a much lower frequency. As a result, I-CSI designs could be applied to scenarios with low mobility or fixed location while, in the cases of short coherence intervals such as high mobility environments, phase shifts tuning based on S-CSI tends to be an advantageous solution. On the ground of these benefits, S-CSI design has attracted a lot of interest [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. For instance, in [2]}, optimal IRS phase shift design was presented based on maximization of the ergodic rate. Further, in [3]}, the authors studied IRS-assisted multi-pair systems and applied a genetic algorithm during the phase shifts optimization.
Taking into account for random matrix theory, the authors in [7]} studied the minimum signal-to-interference-plus-noise ratio (SINR) maximization. In [8]}, a novel two-timescale beamforming
optimization scheme was proposed, where first S-CSI was used to optimize the passive beamforming, and then I-CSI was used to design the active beamforming. In [9]}, both IRS and additive transceiver hardware impairments (HIs) were studied. Note that IRS HIs appear due to the lack of infinite precision at the IRS phase shifts [17]}. In [11]}, two insightful scenarios, namely, a finite number of large IRS and a large number of finite size IRS were considered towards deriving the coverage probability and it was shown that the latter implementation method is more advantageous.
